Clients can use PayPal or a credit card as a billing method. Some clients located in the USA may have ACH available as a billing method. Unfortunately, you can't use the balance on your freelancer account and you can't deposit money to your client account in order to pay your freelancers.

You should be able to verify the credit card you are adding and have authorization to use it. For example you can use you business or company credit card. Sometimes the team may request additional verification to confirm that the client is authorized to use the credit card.

I think you are referring to Roles and Permissions, in which the Admin of the account can manage payment methods, view financial reports, and make deposits and withdrawals. You may check the article I linked on this reply to know how you can add team members in such capacity.

So did you have to add the other person as a financier / team member to your account first, or were you able to add just their credit card to your account and get the payment method verified (on its own), without having to include them as a team member?

Kate/Pandora, as a client who has already done this I can confirm that the name on your payment method does not have to match the name on your client account. All the payment methods on my account are in my CEO's name. As long as you have access to the payment method and can verify it, it's perfectly fine. (I assume that if Upwork see some other suspicious behavior they may ask for "further verification" as a mod mentioned but I've never done anything else.)